document.write( "Question 1046263: what is the minimum value of sin^2(x)+cos^2(x)+sec^2(x)+cosec^2(x)+tan^2(x)+cot^2(x) \n" ); document.write( "

Algebra.Com's Answer #661796 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
what is the minimum value of sin^2(x)+cos^2(x)+sec^2(x)+cosec^2(x)+tan^2(x)+cot^2(x)
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let me introduce c = cos(x) and s = sin(x) for brevity.\r\n" );
document.write( "\r\n" );
document.write( "Then\r\n" );
document.write( "\r\n" );
document.write( " =\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "=  +  +  +  +  =    ( replace    by  1)\r\n" );
document.write( "\r\n" );
document.write( "=  =  +  +  = \r\n" );
document.write( "\r\n" );
document.write( "=  +  +  =  +  +  =  +  -  = .\r\n" );
document.write( "\r\n" );
document.write( "Now,   =  =  =  has the maximum .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore,    has the minimum equal to  = 8 - 1 = 7.\r\n" );
document.write( "\r\n" );
document.write( "Answer.    has the minimum of 7.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \r\n" ); document.write( " \r\n" ); document.write( " \r\n" ); document.write( " \r\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Plot y =

\r
\n" ); document.write( "\n" ); document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );